The conclusion of a reduction need not be surprising. Suppose I am trying to prove that 2+3 =5. I might proceed as follows: Assume that 2+3 does not equal 5. Since 2 = 1+1, and 3 = 1+1+1, that would mean that (1+1) + (1+1+1) does not equal 5. But (1+1) + (1+1+1) does equal 5. So our original assumption must be false, in other words, 2+3=5.

This example isn't that interesting, but the point is to show that you can use the reductio strategy without ending up with a surprising conclusion.

A reductio ad absurdum argument has the following form: we assume that X is true, deduce some absurdity from it, and then conclude that not-X must be true after all. You can view reductio as a rule of inference that allows us to infer not-X from our derivation of an absurdity from X. Why does this work? Because deduction is a process that leads from true assumptions to true conclusions. (See also here.) But an absurdity cannot be true. Therefore, our assumption X is not true. But either X is true or not-X is true. Consequently, it must be not-X that's true.

I agree with Amy that the final upshot of a reductio argument needn't be surprising, so I'll interpret the question differently. Perhaps you're asking the following: when we deduce our absurdity, how do we know whether it's so absurd that we have no choice but to consider it false and thus to conclude, by reductio, not-X — or whether instead to conclude that, contrary to what one might have thought, the alleged absurdity is true after all! You might say, one man's reductio is another's surprising discovery.

The conclusion that not-X must be true is only as strong as one's judgment that the deduced absurdity is false. Typically, in mathematics or logic, that judgment is indubitable because the absurdity is a contradiction (and contradictions are always false); as that rule of inference is employed in logic and mathematics, nothing short of deducing a contradiction would allow it to be applied. Outside those disciplines, however, the absurdity might fall short of a contradiction. The absurdity will often be a claim that is inconsistent with what the proponent of the argument takes to be obviously true. But if someone presented with the argument chooses instead to revise his beliefs in such a way as to permit embrace of the alleged absurdity, there's nothing in the argument itself that can stop him. More general considerations about what it is to be reasonable would have to enter into the picture at that point.

The crucial question is which is more plausible: the premise or the negation of the conclusion. Our answer may be influenced by diverse features of our broader 'web of belief'.